The forward order laws for {1, 2, 3}-and {1, 2, 4}-inverses of a three matrix products


Zhongshan Liu, Zhiping Xiong




In this article, we study the forward order laws for {1, 2, 3}-and {1, 2, 4}-inverses of a product of three matrices by using the maximal and minimal ranks of the generalized Schur complement. The necessary and sufficient conditions for A 1 {1, 2, 3}A 2 {1, 2, 3}A 3 {1, 2, 3} ⊆ (A 1 A 2 A 3){1, 2, 3} and A 1 {1, 2, 4}A 2 {1, 2, 4}A 3 {1, 2, 4} ⊆ (A 1 A 2 A 3){1, 2, 4} are presented.